If $f(x)=\begin{cases} a+bx,& \text{when } x \lt 1\\ 4, & \text{when } x=1 \\b-ax, & \text{when } x \gt 1 \end{cases}$
Find the value of `a` and `b` if `lim_{x \to 1} f(x) = f(1)`.